Peter C. Austin develops methods for observational studies, including propensity score matching. In his simulation study of caliper matching, treated and untreated people are paired only when their scores are sufficiently close.[ref]
The caliper creates a practical tradeoff: a wider tolerance can retain more pairs but allow larger differences in measured baseline risk; a tighter tolerance can discard people and change the population represented by the comparison. Austin compared resulting bias, mean squared error and confidence interval coverage under specified data-generating scenarios. His numerical recommendations concern those estimands and scenarios, rather than a guarantee that matching removes unmeasured confounding.[ref]
Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies by Peter C. Austin. Abstract, continuous and binary outcomes and simulation performance measures
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